Geodesic
Portrait of the roots of a system of equations
Matematičeskoe obrazovanie, Tome 103 (2022) no. 3, pp. 33-46.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article describes a new unusual approach to assessing the quality of numerical optimization methods and solving systems of equations, based on the analysis of areas of attraction of singular points - extrema and roots. Along the way, objects of modern fine art (design) with mathematical and even mystical meanings are generated. A specific system of equations is considered as a person from whom a portrait is being painted. The applied methods of numerical solution of the system of equations are the individual styles of a particular artist. 
@article{MO_2022_103_3_a3,
     author = {V. F. Ochkov and Yu. V. Chudova and N. R. Umirova},
     title = {Portrait of the roots of a system of equations},
     journal = {Matemati\v{c}eskoe obrazovanie},
     pages = {33--46},
     publisher = {mathdoc},
     volume = {103},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MO_2022_103_3_a3/}
}
TY  - JOUR
AU  - V. F. Ochkov
AU  - Yu. V. Chudova
AU  - N. R. Umirova
TI  - Portrait of the roots of a system of equations
JO  - Matematičeskoe obrazovanie
PY  - 2022
SP  - 33
EP  - 46
VL  - 103
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MO_2022_103_3_a3/
LA  - ru
ID  - MO_2022_103_3_a3
ER  - 
%0 Journal Article
%A V. F. Ochkov
%A Yu. V. Chudova
%A N. R. Umirova
%T Portrait of the roots of a system of equations
%J Matematičeskoe obrazovanie
%D 2022
%P 33-46
%V 103
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MO_2022_103_3_a3/
%G ru
%F MO_2022_103_3_a3
V. F. Ochkov; Yu. V. Chudova; N. R. Umirova. Portrait of the roots of a system of equations. Matematičeskoe obrazovanie, Tome 103 (2022) no. 3, pp. 33-46. http://geodesic.mathdoc.fr/item/MO_2022_103_3_a3/

[1] V. F. Ochkov, “Reshenie algebraicheskikh uravnenii i sistem ili Van Gog v srede Mathcad”, KompyuterPress., 2001, no. 9 <ext-link ext-link-type='uri' href='http://www.twt.mpei.ac.ru/ochkov/Carpet/index.htm'>http://www.twt.mpei.ac.ru/ochkov/Carpet/index.htm</ext-link>

[2] V. F. Ochkov, A. V. Bobryakov, S. N. Khorkov, “Gibridnoe reshenie zadach na kompyutere”, Cloud of Science, 4:2 (2017), 5–26 <ext-link ext-link-type='uri' href='http://twt.mpei.ac.ru/ochkov/Hybrid.pdf'>http://twt.mpei.ac.ru/ochkov/Hybrid.pdf</ext-link>

[3] Maarten van Turnhout, Florian Bociort, “Chaotic behavior in an algorithm to escape from poor local minima in lens design”, Opt. Express, 17 (2009), 6436–6450 <ext-link ext-link-type='uri' href='https://opg.optica.org/oe/fulltext.cfm?uri=oe-17-8-6436'>https://opg.optica.org/oe/fulltext.cfm?uri=oe-17-8-6436</ext-link>